Research into the social cost of carbon emissions - the marginal social damage from a tonne of emitted carbon - has tended to focus on best guess scenarios. Such scenarios generally ignore the potential for low-probability, high-damage events, which are critically important to determining optimal climate policy. This paper uses the FUND integrated assessment model to investigate the influence of three types of low-probability, high-impact climate responses on the social cost of carbon: the collapse of the Atlantic Ocean Meridional Overturning Circulation; large scale dissociation of oceanic methane hydrates; and climate sensitivities above best guess levels. We find that incorporating these events can increase the social cost of carbon by a factor of over 3.